Subgroups — C₂₃×#60088 #19207714

Order 5888.

4810 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2898	C₂	1	16	yes	maximal, complemented
5	C₂₃×#2896	C₂	1	6	yes	maximal, complemented
6	C₂×C₂₃×#419	C₂	1	6	yes	maximal, complemented
7	C₂×C₂₃×2₋¹⁺⁴	—	2	8	no	—
8	C₂×C₂₃×2₋¹⁺⁴	—	2	4	no	—
9	C₂×C₂₃×2₋¹⁺⁴	C₄	1	16	yes	complemented
10	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	8	yes	—
11	C₂²×#41×C₂₃	—	2	3	no	—
12	C₂²×#41×C₂₃	C₂²	1	3	yes	—
13	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₂₃	—	2	1	no	—
15	C₂³×Q₈×C₂₃	C₂²	1	3	yes	—
16	C₂₃×#568	—	2	8	no	—
17	C₂×C₂₃×#131	C₂²	1	8	yes	complemented
18	C₂²×M₁₆×C₂₃	C₂²	1	6	yes	—
19	C₂₃×#520	C₂²	1	8	yes	complemented
20	C₂₃×#519	—	2	1	no	—
21	C₂₃×#518	—	2	3	no	—
22	C₄×#41×C₂₃	—	2	4	no	—
23	C₂×C₂₃×#117	C₂²	1	6	yes	—
24	C₂₃×#419	C₂²	1	12	yes	—
25	C₂₃×#419	C₂²	1	24	yes	complemented
26	C₂₃×#418	C₂²	1	4	yes	—
27	C₂₃×#417	C₂²	1	24	yes	complemented
28	C₂₃×#416	C₂²	1	24	yes	complemented
29	C₂×C₂₃×#103	C₂²	1	24	yes	complemented
30	C₂₃×2₋¹⁺⁴	—	2	64	no	—
31	C₂₃×2₋¹⁺⁴	—	2	32	no	—
32	C₂₃×2₋¹⁺⁴	C₂×C₄	1	64	yes	complemented
33	C₂×#41×C₂₃	—	2	48	no	—
34	C₂×#41×C₂₃	—	2	24	no	—
35	C₂×#41×C₂₃	—	2	12	no	—
36	C₂×#41×C₂₃	—	2	6	no	—
37	C₂×#41×C₂₃	C₂×C₄	1	8	yes	—
38	C₂×#41×C₂₃	C₂×C₄	1	24	yes	complemented
39	C₂×#41×C₂₃	D₄	1	8	yes	—
40	C₂×#41×C₂₃	D₄	1	4	yes	—
41	C₂×#41×C₂₃	C₂³	1	12	yes	—
42	C₂×#41×C₂₃	C₂³	1	4	yes	—
43	C₂²×Q₈×C₂₃	—	2	16	no	—
44	C₂²×Q₈×C₂₃	—	2	8	no	—
45	C₂²×Q₈×C₂₃	—	2	3	no	—
46	C₂²×Q₈×C₂₃	—	2	12	no	—
47	C₂²×Q₈×C₂₃	—	2	6	no	—
48	C₂²×Q₈×C₂₃	C₂×C₄	1	24	yes	complemented
49	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
51	C₂²×Q₈×C₂₃	C₂³	1	12	yes	—
52	C₂²×D₄×C₂₃	—	2	3	no	—
53	C₂²×D₄×C₂₃	D₄	1	3	yes	—
54	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₂₃	—	2	3	no	—
56	C₂³×C₄×C₂₃	—	2	3	no	—
57	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
58	C₂₃×#131	—	2	32	no	—
59	C₂×M₁₆×C₂₃	—	2	24	no	—
60	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
61	C₂×M₁₆×C₂₃	C₂³	1	12	yes	—
62	C₂²×C₈×C₂₃	C₂³	1	12	yes	—
63	C₄×Q₈×C₂₃	—	2	8	no	—
64	C₄×D₄×C₂₃	—	2	24	no	—
65	C₂₃×#117	—	2	6	no	—
66	C₂₃×#117	—	2	6	no	—
67	C₂₃×#117	C₂³	1	12	yes	—
68	C₂₃×#117	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₂₃	C₂³	1	12	yes	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	6	no	—
71	C₂×C₄²×C₂₃	—	2	6	no	—
72	C₂₃×#103	C₂³	1	48	yes	—
73	C₂₃×#102	C₂³	1	16	yes	—
74	C₂⁴×C₂₃	—	2	1	no	—
75	C₂⁴×C₂₃	C₂×D₄	1	3	yes	—
76	#41×C₂₃	—	2	192	no	—
77	#41×C₂₃	—	2	48	no	—
78	#41×C₂₃	—	2	24	no	—
79	#41×C₂₃	C₂²⋊C₄	1	32	yes	—
80	#41×C₂₃	C₂²×C₄	1	48	yes	—
81	#41×C₂₃	C₂²×C₄	1	16	yes	—
82	#41×C₂₃	C₂×D₄	1	16	yes	—
83	C₂×Q₈×C₂₃	—	2	64	no	—
84	C₂×Q₈×C₂₃	—	2	24	no	—
85	C₂×Q₈×C₂₃	—	2	48	no	—
86	C₂×Q₈×C₂₃	—	2	6	no	—
87	C₂×Q₈×C₂₃	—	2	3	no	—
88	C₂×Q₈×C₂₃	—	2	12	no	—
89	C₂×Q₈×C₂₃	—	2	24	no	—
90	C₂×Q₈×C₂₃	C₂²⋊C₄	1	8	yes	—
91	C₂×Q₈×C₂₃	C₂²×C₄	1	12	yes	—
92	C₂×Q₈×C₂₃	C₂²×C₄	1	48	yes	—
93	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
94	C₂×Q₈×C₂₃	C₂⁴	1	6	yes	—
95	C₂×D₄×C₂₃	—	2	24	no	—
96	C₂×D₄×C₂₃	—	2	12	no	—
97	C₂×D₄×C₂₃	—	2	1	no	—
98	C₂×D₄×C₂₃	—	2	2	no	—
99	C₂×D₄×C₂₃	C₂²⋊C₄	1	24	yes	—
100	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
101	C₂×D₄×C₂₃	C₂×D₄	1	12	yes	—
102	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₂₃	—	2	24	no	—
104	C₂²×C₄×C₂₃	—	2	3	no	—
105	C₂²×C₄×C₂₃	—	2	12	no	—
106	C₂²×C₄×C₂₃	—	2	24	no	—
107	C₂²×C₄×C₂₃	—	2	12	no	—
108	C₂²×C₄×C₂₃	—	2	12	no	—
109	C₂²×C₄×C₂₃	C₂²×C₄	1	12	yes	—
110	C₂²×C₄×C₂₃	C₂×D₄	1	6	yes	—
111	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
112	C₂²×C₄×C₂₃	C₂×D₄	1	12	yes	—
113	C₂²×C₄×C₂₃	C₂⁴	1	6	yes	—
114	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
115	M₁₆×C₂₃	—	2	8	no	—
116	M₁₆×C₂₃	—	2	24	no	—
117	C₂×C₈×C₂₃	—	2	24	no	—
118	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
119	C₄⋊C₄×C₂₃	—	2	12	no	—
120	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
121	C₂²⋊C₄×C₂₃	—	2	4	no	—
122	C₂²⋊C₄×C₂₃	—	2	12	no	—
123	C₄²×C₂₃	—	2	4	no	—
124	C₄²×C₂₃	—	2	12	no	—
125	#60088	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₂₃	—	2	4	no	—
127	C₂³×C₂₃	—	2	2	no	—
128	C₂³×C₂₃	—	4	6	no	—
129	C₂³×C₂₃	—	4	4	no	—
130	C₂³×C₂₃	C₂×C₂²⋊C₄	1	12	yes	—
131	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
132	C₂³×C₂₃	C₂²×D₄	1	6	yes	—
133	Q₈×C₂₃	—	2	48	no	—
134	Q₈×C₂₃	—	2	12	no	—
135	Q₈×C₂₃	—	2	6	no	—
136	Q₈×C₂₃	C₂×C₂²⋊C₄	1	16	yes	—
137	Q₈×C₂₃	C₂³×C₄	1	12	yes	—
138	D₄×C₂₃	—	2	48	no	—
139	D₄×C₂₃	—	2	4	no	—
140	D₄×C₂₃	—	2	2	no	—
141	D₄×C₂₃	C₂×C₂²⋊C₄	1	48	yes	—
142	D₄×C₂₃	C₂³×C₄	1	4	yes	—
143	C₂×C₄×C₂₃	—	2	12	no	—
144	C₂×C₄×C₂₃	—	2	48	no	—
145	C₂×C₄×C₂₃	—	2	6	no	—
146	C₂×C₄×C₂₃	—	2	48	no	—
147	C₂×C₄×C₂₃	—	2	8	no	—
148	C₂×C₄×C₂₃	—	8	12	no	—
149	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	12	yes	—
150	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	24	yes	—
151	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
152	C₂×C₄×C₂₃	C₂³×C₄	1	12	yes	—
153	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
155	C₂×C₄×C₂₃	C₂²×D₄	1	12	yes	—
156	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
157	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
158	C₈×C₂₃	—	2	8	no	—
159	C₂²×2₋¹⁺⁴	C₂×C₂₃	1	1	yes	characteristic
160	C₂×#568	C₂×C₂₃	1	1	yes	characteristic, complemented
161	#3428	C₂×C₂₃	1	1	yes	characteristic, complemented
162	#2898	C₂×C₂₃	1	16	yes	complemented
163	#2896	C₂×C₂₃	1	6	yes	complemented
164	C₂×#419	C₂×C₂₃	1	6	yes	complemented
165	C₂²×C₂₃	—	2	12	no	—
166	C₂²×C₂₃	—	2	2	no	—
167	C₂²×C₂₃	—	2	4	no	—
168	C₂²×C₂₃	—	4	12	no	—
169	C₂²×C₂₃	—	4	8	no	—
170	C₂²×C₂₃	—	4	4	no	—
171	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	2	yes	—
172	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	12	yes	—
173	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
174	C₄×C₂₃	—	2	12	no	—
175	C₄×C₂₃	—	4	8	no	—
176	C₄×C₂₃	C₂²×C₂²⋊C₄	1	12	yes	—
177	C₄×C₂₃	C₂²×C₂²⋊C₄	1	2	yes	—
178	C₄×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
179	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
180	C₂×2₋¹⁺⁴	—	2	8	no	—
181	C₂×2₋¹⁺⁴	—	2	4	no	—
182	C₂×2₋¹⁺⁴	C₄×C₂₃	1	16	yes	complemented
183	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	8	yes	—
184	C₂²×#41	—	2	3	no	—
185	C₂²×#41	C₂²×C₂₃	1	3	yes	—
186	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
187	C₂³×Q₈	—	2	1	no	—
188	C₂³×Q₈	C₂²×C₂₃	1	3	yes	—
189	#568	—	2	8	no	—
190	C₂×#131	C₂²×C₂₃	1	8	yes	complemented
191	C₂²×M₁₆	C₂²×C₂₃	1	6	yes	—
192	#520	C₂²×C₂₃	1	8	yes	complemented
193	#519	—	2	1	no	—
194	#518	—	2	3	no	—
195	C₄×#41	—	2	4	no	—
196	C₂×#117	C₂²×C₂₃	1	6	yes	—
197	#419	C₂²×C₂₃	1	12	yes	—
198	#419	C₂²×C₂₃	1	24	yes	complemented
199	#418	C₂²×C₂₃	1	4	yes	—
200	#417	C₂²×C₂₃	1	24	yes	complemented
201	#416	C₂²×C₂₃	1	24	yes	complemented
202	C₂×#103	C₂²×C₂₃	1	24	yes	complemented
203	C₂×C₂₃	—	2	2	no	—
204	C₂×C₂₃	—	2	12	no	—
205	C₂×C₂₃	—	4	4	no	—
206	C₂×C₂₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₂₃	#3586	1	2	yes	—
208	2₋¹⁺⁴	—	2	64	no	—
209	2₋¹⁺⁴	—	2	32	no	—
210	2₋¹⁺⁴	C₂×C₄×C₂₃	1	64	yes	complemented
211	C₂×#41	—	2	48	no	—
212	C₂×#41	—	2	24	no	—
213	C₂×#41	—	2	12	no	—
214	C₂×#41	—	2	6	no	—
215	C₂×#41	C₂×C₄×C₂₃	1	8	yes	—
216	C₂×#41	C₂×C₄×C₂₃	1	24	yes	complemented
217	C₂×#41	D₄×C₂₃	1	8	yes	—
218	C₂×#41	D₄×C₂₃	1	4	yes	—
219	C₂×#41	C₂³×C₂₃	1	12	yes	—
220	C₂×#41	C₂³×C₂₃	1	4	yes	—
221	C₂²×Q₈	—	2	16	no	—
222	C₂²×Q₈	—	2	8	no	—
223	C₂²×Q₈	—	2	3	no	—
224	C₂²×Q₈	—	2	12	no	—
225	C₂²×Q₈	—	2	6	no	—
226	C₂²×Q₈	C₂×C₄×C₂₃	1	24	yes	complemented
227	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
228	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
229	C₂²×Q₈	C₂³×C₂₃	1	12	yes	—
230	C₂²×D₄	—	2	3	no	—
231	C₂²×D₄	D₄×C₂₃	1	3	yes	—
232	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
233	C₂³×C₄	—	2	3	no	—
234	C₂³×C₄	—	2	3	no	—
235	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
236	#131	—	2	32	no	—
237	C₂×M₁₆	—	2	24	no	—
238	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
239	C₂×M₁₆	C₂³×C₂₃	1	12	yes	—
240	C₂²×C₈	C₂³×C₂₃	1	12	yes	—
241	C₄×Q₈	—	2	8	no	—
242	C₄×D₄	—	2	24	no	—
243	#117	—	2	6	no	—
244	#117	—	2	6	no	—
245	#117	C₂³×C₂₃	1	4	yes	—
246	#117	C₂³×C₂₃	1	12	yes	—
247	C₂×C₄⋊C₄	C₂³×C₂₃	1	12	yes	—
248	C₂×C₂²⋊C₄	—	2	6	no	—
249	C₂×C₄²	—	2	6	no	—
250	#103	C₂³×C₂₃	1	48	yes	—
251	#102	C₂³×C₂₃	1	16	yes	—
252	C₂₃	#60088	1	1	yes	characteristic, direct product factor, Sylow
253	C₂⁴	—	2	1	no	—
254	C₂⁴	C₂×D₄×C₂₃	1	3	yes	—
255	#41	—	2	192	no	—
256	#41	—	2	48	no	—
257	#41	—	2	24	no	—
258	#41	C₂²⋊C₄×C₂₃	1	32	yes	—
259	#41	C₂²×C₄×C₂₃	1	48	yes	—
260	#41	C₂²×C₄×C₂₃	1	16	yes	—
261	#41	C₂×D₄×C₂₃	1	16	yes	—
262	C₂×Q₈	—	2	64	no	—
263	C₂×Q₈	—	2	24	no	—
264	C₂×Q₈	—	2	48	no	—
265	C₂×Q₈	—	2	3	no	—
266	C₂×Q₈	—	2	12	no	—
267	C₂×Q₈	—	2	6	no	—
268	C₂×Q₈	—	2	24	no	—
269	C₂×Q₈	C₂²⋊C₄×C₂₃	1	8	yes	—
270	C₂×Q₈	C₂²×C₄×C₂₃	1	12	yes	—
271	C₂×Q₈	C₂²×C₄×C₂₃	1	48	yes	—
272	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
273	C₂×Q₈	C₂⁴×C₂₃	1	6	yes	—
274	C₂×D₄	—	2	24	no	—
275	C₂×D₄	—	2	12	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	C₂²⋊C₄×C₂₃	1	24	yes	—
279	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
280	C₂×D₄	C₂×D₄×C₂₃	1	12	yes	—
281	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
282	C₂²×C₄	—	2	24	no	—
283	C₂²×C₄	—	2	3	no	—
284	C₂²×C₄	—	2	12	no	—
285	C₂²×C₄	—	2	24	no	—
286	C₂²×C₄	—	2	12	no	—
287	C₂²×C₄	—	2	12	no	—
288	C₂²×C₄	C₂²×C₄×C₂₃	1	12	yes	—
289	C₂²×C₄	C₂×D₄×C₂₃	1	6	yes	—
290	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
291	C₂²×C₄	C₂×D₄×C₂₃	1	12	yes	—
292	C₂²×C₄	C₂⁴×C₂₃	1	6	yes	—
293	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
294	M₁₆	—	2	8	no	—
295	M₁₆	—	2	24	no	—
296	C₂×C₈	—	2	24	no	—
297	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
298	C₄⋊C₄	—	2	12	no	—
299	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₂²⋊C₄	—	2	12	no	—
302	C₄²	—	2	4	no	—
303	C₄²	—	2	12	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	4	6	no	—
307	C₂³	—	4	4	no	—
308	C₂³	C₂×C₂²⋊C₄×C₂₃	1	12	yes	—
309	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
310	C₂³	C₂²×D₄×C₂₃	1	6	yes	—
311	Q₈	—	2	6	no	—
312	Q₈	—	2	48	no	—
313	Q₈	—	2	12	no	—
314	Q₈	C₂×C₂²⋊C₄×C₂₃	1	16	yes	—
315	Q₈	C₂³×C₄×C₂₃	1	12	yes	—
316	D₄	—	2	48	no	—
317	D₄	—	2	2	no	—
318	D₄	—	2	4	no	—
319	D₄	C₂×C₂²⋊C₄×C₂₃	1	48	yes	—
320	D₄	C₂³×C₄×C₂₃	1	4	yes	—
321	C₂×C₄	—	2	6	no	—
322	C₂×C₄	—	2	12	no	—
323	C₂×C₄	—	2	48	no	—
324	C₂×C₄	—	2	48	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	8	12	no	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	12	yes	—
328	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	24	yes	—
329	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
330	C₂×C₄	C₂³×C₄×C₂₃	1	12	yes	—
331	C₂×C₄	C₂²×D₄×C₂₃	1	12	yes	—
332	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
333	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
334	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
335	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
336	C₈	—	2	8	no	—
337	C₂²	—	2	12	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	4	12	no	—
341	C₂²	—	4	8	no	—
342	C₂²	—	4	4	no	—
343	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	2	yes	—
344	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	12	yes	—
345	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
346	C₄	—	2	12	no	—
347	C₄	—	4	8	no	—
348	C₄	C₂²×C₂²⋊C₄×C₂₃	1	12	yes	—
349	C₄	C₂²×C₂²⋊C₄×C₂₃	1	2	yes	—
350	C₄	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
351	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
352	C₂	—	2	2	no	—
353	C₂	—	2	12	no	—
354	C₂	—	4	4	no	—
355	C₂	C₂³×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
356	C₂	C₂₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂²×C₂₃×2₋¹⁺⁴	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×#41×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₂₃×#568	C₂	semidirect
3. C₂₃×#3428	C₂	semidirect
4. C₂₃×#2898	C₂	semidirect
5. C₂₃×#2896	C₂	semidirect
6. C₂×C₂₃×#419	C₂	semidirect
9. C₂×C₂₃×2₋¹⁺⁴	C₄	semidirect
17. C₂×C₂₃×#131	C₂²	semidirect
19. C₂₃×#520	C₂²	semidirect
25. C₂₃×#419	C₂²	semidirect
27. C₂₃×#417	C₂²	semidirect
28. C₂₃×#416	C₂²	semidirect
29. C₂×C₂₃×#103	C₂²	semidirect
32. C₂₃×2₋¹⁺⁴	C₂×C₄	semidirect
38. C₂×#41×C₂₃	C₂×C₄	semidirect
48. C₂²×Q₈×C₂₃	C₂×C₄	semidirect
125. #60088	C₂₃	direct (N × H)
160. C₂×#568	C₂×C₂₃	semidirect
161. #3428	C₂×C₂₃	semidirect
162. #2898	C₂×C₂₃	semidirect
163. #2896	C₂×C₂₃	semidirect
164. C₂×#419	C₂×C₂₃	semidirect
182. C₂×2₋¹⁺⁴	C₄×C₂₃	semidirect
190. C₂×#131	C₂²×C₂₃	semidirect
192. #520	C₂²×C₂₃	semidirect
198. #419	C₂²×C₂₃	semidirect
200. #417	C₂²×C₂₃	semidirect
201. #416	C₂²×C₂₃	semidirect
202. C₂×#103	C₂²×C₂₃	semidirect
210. 2₋¹⁺⁴	C₂×C₄×C₂₃	semidirect
216. C₂×#41	C₂×C₄×C₂₃	semidirect
226. C₂²×Q₈	C₂×C₄×C₂₃	semidirect
252. C₂₃	#60088	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₂₃×2₋¹⁺⁴	2
C₂×C₂₃×#568	2
C₂₃×#3428	2
C₂₃×#2898	2
C₂₃×#2896	2
C₂×C₂₃×#419	2
#60088	23

Subgroups — C23×#60088 #19207714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60088 #19207714